A combination of heliospheric and solar data was used to identify open magnetic fields stretching from the lower corona to Earth orbit. 35 near-relativistic electron beams detected at the ACE spacecraft "labeled" the heliospheric segments of the open fields. An X-ray flare occurred <20 minutes before injection of the electrons in 25 events. These flares labeled the solar segment of the open fields. The flares occurred in western-hemisphere active regions (ARs) with coronal holes whose polarity agreed with the polarity of the beam-carrying interplanetary fields in 23 of the 25 events. We conclude that electron beams reach 1 AU from open AR fields adjacent to flare sites. The Wang & Sheeley implementation of the potential-field source-surface model successfully identified the open fields in 36% of cases. Success meant that the open fields reached the source surface within 3 heliographic deg of the interplanetary magnetic field connected to ACE at 1 AU. Inclusion of five near misses improves the success rate to 56%. The success rate for the Schrijver & DeRosa PFSS implementation was 50%. Our results suggest that, even if the input magnetic data are updated frequently, the PFSS models succeed in only ~50% of cases to identify the coronal segment of open fields. Development of other techniques is in its infancy.